Calculation of neutron-${}^3\mathrm{He}$ scattering up to 30 MeV

Background: Microscopic calculations of four-body collisions become very challenging in the energy regime above the threshold for four free particles. The neutron-${}^3\mathrm{He}$ scattering is an example of such processes with elastic, rearrangement, and breakup channels.

Purpose: We aim to calculate observables for elastic and inelastic neutron-${}^3\mathrm{He}$ reactions up to 30 MeV neutron energy using realistic nuclear force models.

Methods: We solve the Alt, Grassberger, and Sandhas (AGS) equations for the four-nucleon transition operators in the momentum-space framework. The complex-energy method with special integration weights is applied to deal with the complicated singularities in the kernel of AGS equations.

Results: We obtain fully converged results for the differential cross section and neutron analyzing power in the neutron-${}^3\mathrm{He}$ elastic scattering as well as the total cross sections for inelastic reactions. Several realistic potentials are used, including one with an explicit $\Delta$ isobar excitation.

Conclusions: There is reasonable agreement between the theoretical predictions and experimental data for the neutron-${}^3\mathrm{He}$ scattering in the considered energy regime. The most remarkable disagreements are seen around the minimum of the differential cross section and the extrema of the neutron analyzing power. The breakup cross section increases with energy exceeding rearrangement channels above 23 MeV.

Figure 1

Differential cross section of elastic $n\text{−}{}^3\mathrm{He}$ scattering at neutron energy between 6 and 30 MeV. Results obtained with potentials INOY04 (solid curves), CD Bonn (dotted curves), and CD Bonn + $\Delta$ (dashed-dotted curves) are compared with data from Refs. [33, 34, 35, 36].

Figure 2

Neutron analyzing power of elastic $n\text{−}{}^3\mathrm{He}$ scattering at neutron energy between 8 and 22 MeV. Curves as in Fig. 1. Data are from Refs. [40, 41, 42, 43].

Figure 3

${}^3\mathrm{He}$ target analyzing power $A_{0y}$, $n\text{−}{}^3\mathrm{He}$ spin correlation coefficient $A_{yy}$, and neutron spin transfer coefficient $K_y^y$ for elastic $n+{}^3\mathrm{He}$ scattering at 12 and 22 MeV neutron energy. Curves as in Fig. 1.

Figure 4

Differential cross section of the ${}^3\mathrm{He}(n,p){}^3\mathrm{H}$ reaction at 14.4 MeV neutron energy. Predictions using INOY04 potential are compared with the data from Refs. [36, 44].

Figure 5

Differential cross section of the ${}^3\mathrm{He}(n,d){}^2\mathrm{H}$ reaction at $E_n=14.4$ MeV. Predictions using INOY04 potential are compared with the data from Ref. [36].

Figure 6

$n\text{−}{}^3\mathrm{He}$ total and partial cross sections as functions of the neutron beam energy calculated using the INOY04 potential. The data are from Refs. [33, 46] ($\square$), [34] ($\times$), [35] ($•$), [47] ($▴$), and [48] ($+$).